This invention is in the field of exploration for oil and gas reservoirs, and is more specifically directed to the analysis of seismic survey signals obtained in such exploration.
The use of seismic survey techniques is commonplace in the prospecting for subsurface reservoirs of hydrocarbons such as oil and gas. As is fundamental in the art, seismic surveys are typically obtained by imparting acoustic energy into the earth, either at a land surface or into the water in a marine survey, and detecting the energy at other surface or marine locations away from the source. The detectors sense the arrival of the acoustic energy after reflection from subsurface strata and interfaces, such that the time delay between the imparting of energy by the source and its receipt by the detectors will be indicative of the depth below the earth surface at which the reflecting interface is located. Conversion of the time-domain reflection signals into depth will thus provide a survey of the subsurface geology.
FIG. 1 illustrates a conventional land-based seismic survey, in which a reflective geological interface is present in the earth between subsurface strata 2, 4, along which a particular depth point DP of interest for this description is located. Of course, many depth points will be analyzed along this and other interfaces in a typical survey. As is evident from FIG. 1, multiple source-receiver pairs will impart energy to and receive reflected energy from depth point DP, at varying angles. The so-called "zero-offset" source receiver pair S.sub.0, R.sub.0 corresponds to the case where both the source and detector are directly above depth point DP (i.e., there is no offset distance between receiver R.sub.0 and the surface location directly over depth point DP); typically, the zero-offset signal is not actually obtained, but is instead extrapolated from the non-zero offset traces. Source-receiver pairs S.sub.1, R.sub.1 ; S.sub.2, R.sub.2 ; S.sub.3, R.sub.3 similarly respectively impart energy to and receive reflected energy from depth point DP at varying angles and thus at varying offsets.
A well-known technique in the art for eliminating random noise from the survey signals is referred to as common midpoint (CMP), or common depth point (CDP), gather and stack. In this technique, the signals from each source-receiver path having the same depth point, such as depth point DP in FIG. 1, are selected from the survey data, forming a group of traces known as a CMP (or, equivalently, CDP) gather. Elimination of random noise is then performed by summing the traces in the gather into a "stack". This summation will tend to reinforce the signal portion of the traces corresponding to the reflection event, which should be common among all traces having the same reflection midpoint, while the random noise will tend to cancel in the summation.
However, the traces in the CMP gather of FIG. 1 generally have different reflection times for energy reflected from the same reflection point DP, considering that their source-receiver paths are of different length. For example, the distance along which energy must travel from source S.sub.3 to receiver R.sub.3 is much greater than the distance along which energy must travel in the near-offset pair S.sub.1, R.sub.1, due to the larger angle from the vertical of the path of energy from source S.sub.3 to receiver R.sub.3. In the case of FIG. 1, the trace recorded by receiver R.sub.1 for energy reflecting from depth point DP would be considered as a relatively near offset signal as compared to the trace recorded by receiver R.sub.3 for energy reflecting from the same depth point DP. In the time-domain seismic traces recorded by receivers R.sub.1 and R.sub.3, the time at which energy reflected from depth point DP will appear in the trace for receiver R.sub.3 will be later than the time at which energy reflected from depth point DP is indicated in the trace for nearer-offset receiver R.sub.1.
The time-domain effect of varying offset must be taken into account in the CMP stack process in order for the signal portions of traces of varying offset to properly align and provide an accurate indication of the depth of the reflector. This is typically handled by way of "normal moveout correction", or NMO (also NMOC), in which the traces corresponding to source-receiver paths of various lengths are time-shifted relative to one another so that their detected reflection events are aligned in time. The amount of the time shift for a given trace will, of course, depend upon its offset distance and upon the velocity with which the acoustic energy travels in the strata along the shot-receiver path. Normal moveout correction therefore requires the estimation or determination of a velocity, commonly referred to as the "stacking" velocity, for deriving the necessary time shift as a function of offset. The relationship between offset and the NMO time correction .DELTA.T.sub.x, for a given seismic reflection event in a seismic trace, follows the well-known Dix equation: ##EQU1## where T.sub.0 is the zero offset reflection time of the reflection, X is the offset distance of the trace being corrected, V.sub.g is the stacking velocity for the reflection event, and where .DELTA.T.sub.x is the NMO time shift for the reflection event in the trace being corrected.
Conventional derivation of the stacking velocity V.sub.g for NMO correction is typically done in a "best-fit" manner to optimize the accuracy of the correction among all of the traces in the gather. For example, a series of corrections based upon multiple trial stacking velocities may be applied to a gather of traces. Semblance, or correlation, analysis is then applied among the traces over limited time windows (corresponding to the localities of individual reflection events), and plotted as a function of time T.sub.0 and velocity V.sub.g. The best-fit stacking velocities for each event are then selected at the values yielding the highest semblance value, resulting in a stacking velocity time function V.sub.g (T.sub.0). NMO correction may then be readily applied to each reflection event in each trace, using the stacking velocity function derived from the semblance analysis.
Other conventional techniques for deriving the NMO correction include constant velocity gather (CVG) and constant velocity stack (CVS) analysis. These techniques assume that the seismic velocity is constant along the paths associated with the same reflection interface, and calculate the NMO correction for each trace as a function of two-way time. The best NMO correction may then be readily selected as that which shows a flat reflector over a series of traces of varying offset for each CMP gather.
The accuracy of these conventional approaches in deriving and applying NMO correction depends upon the fidelity of the reflection signal across the traces in the CMP gather. In particular, conventional NMO techniques rely upon reflection signals in the traces having substantially the same phase, so that sufficient signal correlation will be present among the traces to provide meaningful selection of the proper NMO correction. It has been observed, however, in connection with the present invention, that seismic waves are distorted not only in time and amplitude as a function of offset, but are also distorted in phase during propagation through the subsurface.
FIG. 2 illustrates an example of phase distortion as a function of offset in a seismic survey. Trace S.sub.n is a near-offset trace illustrating a reflection event E.sub.n that is centered about a two-way time T. Reflection event E.sub.n exhibits a high positive amplitude that is symmetric about time T, and as such provides a strong reflection signal. Trace S.sub.f is a far-offset trace in the same CMP gather as trace S.sub.n, and as such has a reflection event E.sub.f caused by energy reflecting from the same subsurface reflector as reflection event E.sub.n of trace S.sub.n. As expected for trace S.sub.f, which is at a larger offset distance than trace S.sub.n, reflection event E.sub.f appears at a delayed time T+.DELTA.T; in this example, .DELTA.T corresponds to the relative NMO time-shift correction that would be applied to trace S.sub.f prior to stacking it with trace S.sub.n.
As exhibited in FIG. 2, however, not only is reflection event R.sub.f delayed in time from reflection event E.sub.n, but reflection event E.sub.f also has significant phase distortion relative to reflection event E.sub.n, such that its positive amplitude pulse lags its central point in time at time T+.DELTA.T. As a result, the simple stacking of trace S.sub.f with trace S.sub.n would result in a distorted stacked signal; this offset-dependent phase distortion, especially when present on many traces in a CMP gather, also adversely affects the determination of the proper stacking velocity and the NMO correction itself. Accordingly, phase distortion has been observed to significantly degrade the signal-to-noise ratio of seismic surveys.
In the frequency domain, the dispersive phase behavior of seismic signals over frequency has a frequency-dependent slope that is also dependent upon the two-way time, as is well known. Referring now to FIG. 3, an exemplary dispersive phase spectrum .PHI..sub.0 (f) for a zero-phase shift signal is illustrated. This zero-phase shift spectrum .PHI..sub.0 (f) may be approximated as a linear function of frequency, expressed as: EQU .PHI..sub.0 (f)=(-2.pi.)f.DELTA.T.sub.x
where .DELTA.T.sub.x is the NMO correction from zero for the particular trace. Accordingly, the slope of the dispersive phase spectrum is proportional to the NMO correction for the trace.
The effects of phase distortion in a seismic trace discussed above may also be seen in FIG. 3. Spectrum .PHI..sub..DELTA. (f) is the dispersive phase spectrum of a trace in which a zero-frequency phase shift .PHI..sub..DELTA. (0) is present; trace S.sub.f of FIG. 2 is an example of such a trace. The slope of linearly-approximated spectrum .PHI..sub..DELTA. (f) is the same as in the case of zero-phase shift approximated spectrum .PHI..sub.0 (f) in other words, the correct NMO time-shift correction that is to be applied to the trace is independent of phase.
However, as noted above, conventional NMO correction techniques assume that no offset-dependent phase shift exists and thus, with reference to FIG. 3, assumes that the dispersive phase spectrum passes through the origin of the phase-frequency plot. As a result, conventional NMO correction techniques can produce different NMO correction values for the same event of the same trace, depending upon the dominant frequency considered. For example, if the trace and event giving rise to spectrum .PHI..sub..DELTA. (f) of FIG. 3 is analyzed at frequency f.sub.1, a slope NMOC.sub.1 is found that passes through the origin; analysis at frequency f.sub.2 gives a different, flatter, slope NMOC.sub.2 for this same event and trace. Not only do the slopes, or corrections, NMOC.sub.1, NMOC.sub.2 differ depending upon the frequency of analysis, but neither of the corrections that are derived using a zero-phase shift assumption for a phase-shifted event provide an accurate NMO correction.
It is therefore an object of the present invention to provide a method of normal moveout correction that accounts for offset-dependent phase shifts in seismic signals.
It is a further object of the present invention to provide such a method that enables subsequent data stacking and migration to be correct over a wider frequency band.
It is a further object of the present invention to provide such a method that may be implemented into an automated system.
By way of further background, it is well known, as described in Shapiro et al., "Frequency-dependent anisotropy of scalar waves in a multilayered medium", J. Seismic Exploration, 3 (1994), pp. 37-52, that layer stratification in formations such as shale and limestone causes anisotropic attenuation of acoustic energy, such that the attenuation of the energy by the formation is dependent upon the angle of incidence.
It is therefore a further object of the present invention to provide a method of analyzing phase dispersion of reflected energy in such a manner as to assist in the interpretation of the composition of a reflecting stratum.
Other objects and advantages of the present invention will be apparent to those of ordinary skill in the art having reference to the following specification together with its drawings.